sampling.awk

# Input 1: a vector of n probabilities each 0 < p < 1 such that sum of all p = k
# Input 2: k - integer
# Output: all possible products of Pi where k of Pi are selected as such, the other n-k as (1-Pi)
# Run as: awk -f sampling.R

BEGIN {
	n = 5;
	k = 2;
	p[1] = 0.15;
	p[2] = 0.22;
	p[3] = 0.36;
	p[4] = 0.56;
	p[5] = 0.71;
	p_prod(1, k, 1, "");
}

function p_prod(start, kk, curr_prod, path) {
		if (start > n) {
			if (kk <= 0) {
				printf "%10.8f; %s\n\r", curr_prod, path;
			}
		}
		else {
			if (kk > 0) {
				cc = curr_prod * (p[start]+0);
				pp = path " (+" start ", " p[start] ", " curr_prod ")";
				p_prod(start+1, kk-1, cc, pp);
			}
			cc = curr_prod * (1 - (p[start]+0));
			pp = path " (-" start ", " (1 - p[start]) ", " curr_prod ")";
			p_prod(start+1, kk, cc, pp);
		}
}